This is a maths problem really, solved by V=S.

So (4/3)π(r^3) = 4π(r^2)

r^2 can be cancelled from both sides to give:

(4/3)πr = 4π

Then there is only one variable that can be separated by dividing both sides by 4π to give:

(1/3)r = 1

Then times both sides by three to give r=3.

Diameter is equal to 2r as @uber-dragon mentioned so diameter =6.


So no winners here, I've learnt my lesson and will do easier problems :P